Quantum Calculations Can Make Atomic Clocks of the Future Far More Accurate

New calculations of how atoms swell when they’re warmed up can help make the next generation of atomic clocks 10 times more precise.

The current precision champ, the quantum-logic clock developed last year at the National Institute for Standards and Technology in Boulder, Colorado, keeps time to within a second every 3.7 billion years. Future clocks that use the new improvements would be accurate to a second every 32 billion years — more than twice the age of the universe.

Such ultra-precise clocks are based on the quick vibrations of a single aluminum ion, an atom that has lost one electron, held in a vacuum and confined by electromagnetic fields. The remaining electrons form a shell around the atom’s nucleus.

“With a laser pulse, you can tap that shell and make it ring like a bell,” said physicist Till Rosenband of NIST, who built the existing quantum-logic clock. Bu a bell vibrates a mere few hundred times a second, in the range of human hearing, the aluminum ion vibrates at 1.1 quadrillion times a second. These vibrations turn the ion into a sort of superfast metronome.

“Because it’s ringing so fast, it’s dividing time into much smaller intervals,” Rosenband said. “That allows it to keep time very precisely.”

Unfortunately, the standard definition of a second relies on what the atom does at a temperature of absolute zero. Real clocks need to run at room temperature, where the shell of electrons puffs up.

“You may not notice it, but it’s there,” Rosenband said. “The aluminum ion feels it, too.” The heated ion vibrates at a slightly different frequency, making the clock a little less accurate. Until now, physicists didn’t know how much less accurate it was.

“For the next generation of aluminum-ion clock, I think it’s essential to know what that shift is,” said physicist Marianna Safronova of the University of Delaware, lead author of the new study. The results were presented May 6 at the Conference on Lasers and Electro-Optics in Baltimore.

Because of peculiarities in its atomic structure, aluminum is particularly insensitive to temperature shifts — about 1,000 times less sensitive than strontium, one of the other leading candidates for atomic clocks. But its insensitivity means the shift is almost too small to measure and complicated to calculate.

By combining two different techniques in a new way, Safronova and colleagues developed a novel approach for calculating the shift based on fundamental physics. One technique considered the way the two outermost electrons in the aluminum ion interact with each other, and the other considered how those electrons interact with the inner electrons and the nucleus.

“We did them from first principles, from a basic understanding of quantum mechanics and atoms, without putting any experimental inputs to adjust the calculations,” Safronova said.

The new calculation shows that at room temperature, the aluminum-ion clock is sensitive to changes in temperature of 57 sextillionths of a degree Celsius, or 5.7 x 10-20 degrees. A quartz wristwatch, by comparison, is sensitive to about a millionth of a degree, or 10-6 degrees.

The calculation reduces the uncertainty in the clock’s ticking to 4 x 10-19, an order of magnitude better than the current clocks can achieve.

“We’re working on a new version of this clock right now,” Rosenband said. There are still other uncertainties that need to be worked out, mostly due to the atom’s slight motion in its electric field trap, before the researchers will be satisfied. “But the black body shift is an important one. That one has been put to bed, more or less, by this work. So we can concentrate more on other effects. This calculation will make that new clock more accurate and more useful for that reason.”

Building ever-more accurate clocks could help answer questions about fundamental physics, improve GPS systems, predict earthquakes and test Einstein’s relativity, among other things, the researchers said.

“You can build better gravity sensors. You can see fundamental laws of physics change with time,” Safronova said. “Ultra-precise navigation, tracking of deep space probes — there are a lot of applications to this high precision timekeeping.”

Image: The ion trap makes the heart of the aluminum-ion clock. (National Institute for Standards and Technology)